Embedding crossed cube into diverse product graphs and tree-derived architectures

Paul Immanuel () and A. Berin Greeni ()
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Paul Immanuel: Vellore Institute of Technology
A. Berin Greeni: Vellore Institute of Technology

Journal of Combinatorial Optimization, 2025, vol. 50, issue 2, No 7, 21 pages

Abstract: Abstract The embedding of graphs plays a vital role in simulating parallel architectures into other parallel topologies. Out of all parallel computing architectures in super-computing, hypercube, and its variants cannot be ignored because of the desirable, easily implementable, and applicable properties. One such variant of hypercube is the crossed cube $$CQ^r$$ . With exponential growth in the layout of VLSI designs, the concept of embedding has attained paramount importance. Crossed cube, a highly cited one among the variants of hypercube is explored with respect to embedding in this work. As a sequel, we derive the exact wirelength of embedding crossed cube into certain tree-derived architectures, corona product of a path on $$2^{r-1}$$ nodes into an isolated node (comb), Cartesian product of path on 2 nodes into a path on $$2^{r-1}$$ nodes (ladder) and path (MinLA).

Keywords: Embedding; Wirelength; Crossed cube (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10878-025-01350-y

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